Alarm would not turn off, disconnected alarm box under dash and now car will not start

It will not start with the box disconnected. The only way to repair it is to determine why the alarm sounded. Common issues are a defective hood switch or the switch in the latch that is supposed to disarm the system. The problem is that even with the module plugged in the car will likely not start as the alarm is activated. If you connect it all back up and use the key do the doors lock and unlock from the outside using the drivers door key? That would show you if the Black ground wire is okay. Because this is a 1994 you won't get the indicators in a scan tool telling you which door tripped the alarm, but because it happened when you used the key in that door it is likely the switch inside the door latch itself that is the issue.
Do you use the key to lock unlock it normally or a fob?
Is this a factory installed alarm or was it a dealer option unit? Does it have a remote that works?